Cross sections for the reactionse+e−→K+K−π+π−,K+K−π0π0, andK+K−K+K−measured using initial-state radiation events

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Abstract

We study the processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$, ${K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$, and ${K}^{+}{K}^{\ensuremath{-}}{K}^{+}{K}^{\ensuremath{-}}\ensuremath{\gamma}$, where the photon is radiated from the initial state. About 84 000, 8000, and 4200 fully reconstructed events, respectively, are selected from $454\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of BABAR data. The invariant mass of the hadronic final state defines the ${e}^{+}{e}^{\ensuremath{-}}$ center-of-mass energy, so that the ${K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ data can be compared with direct measurements of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ reaction. No direct measurements exist for the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ or ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{+}{K}^{\ensuremath{-}}$ reactions, and we present an update of our previous result based on a data sample that is twice as large. Studying the structure of these events, we find contributions from a number of intermediate states and extract their cross sections. In particular, we perform a more detailed study of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\phi}(1020)\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\gamma}$ reaction and confirm the presence of the $Y(2175)$ resonance in the $\ensuremath{\phi}(1020){f}_{0}(980)$ and ${K}^{+}{K}^{\ensuremath{-}}{f}_{0}(980)$ modes. In the charmonium region, we observe the $J/\ensuremath{\psi}$ in all three final states and in several intermediate states, as well as the $\ensuremath{\psi}(2S)$ in some modes, and measure the corresponding products of branching fraction and electron width.

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